scholarly journals Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 257 ◽  
Author(s):  
Filip B. Maciejewski ◽  
Zoltán Zimborás ◽  
Michał Oszmaniec
Keyword(s):  
Quantum Algorithms ◽  
Probability Distributions ◽  
Post Processing ◽  
Measurement Device ◽  
Quantum Devices ◽  
Quantum Process ◽  
Error Mitigation ◽  
Process Tomography ◽  
State Tomography ◽  
Near Term

We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement device. If the measurement device is affected only by an invertible classical noise, it is possible to correct the outcome statistics of future experiments performed on the same device. To support the practical applicability of this scheme for near-term quantum devices, we characterize measurements implemented in IBM's and Rigetti's quantum processors. We find that for these devices, based on superconducting transmon qubits, classical noise is indeed the dominant source of readout errors. Moreover, we analyze the influence of the presence of coherent errors and finite statistics on the performance of our error-mitigation procedure. Applying our scheme on the IBM's 5-qubit device, we observe a significant improvement of the results of a number of single- and two-qubit tasks including Quantum State Tomography (QST), Quantum Process Tomography (QPT), the implementation of non-projective measurements, and certain quantum algorithms (Grover's search and the Bernstein-Vazirani algorithm). Finally, we present results showing improvement for the implementation of certain probability distributions in the case of five qubits.

scholarly journals Algorithmic Error Mitigation Scheme for Current Quantum Processors

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 492
Author(s):  
Philippe Suchsland ◽  
Francesco Tacchino ◽  
Mark H. Fischer ◽  
Titus Neupert ◽  
Panagiotis Kl. Barkoutsos ◽  
...  
Keyword(s):  
Quantum Chemistry ◽  
Ground State ◽  
State Of The Art ◽  
Quantum Algorithms ◽  
Quantum Circuit ◽  
Lanczos Method ◽  
Error Mitigation ◽  
Near Term ◽  
The Impact ◽  
Different Sources

We present a hardware agnostic error mitigation algorithm for near term quantum processors inspired by the classical Lanczos method. This technique can reduce the impact of different sources of noise at the sole cost of an increase in the number of measurements to be performed on the target quantum circuit, without additional experimental overhead. We demonstrate through numerical simulations and experiments on IBM Quantum hardware that the proposed scheme significantly increases the accuracy of cost functions evaluations within the framework of variational quantum algorithms, thus leading to improved ground-state calculations for quantum chemistry and physics problems beyond state-of-the-art results.

scholarly journals Variational Quantum Computation of Excited States

Quantum ◽  
2019 ◽  
Vol 3 ◽  
pp. 156 ◽  
Author(s):  
Oscar Higgott ◽  
Daochen Wang ◽  
Stephen Brierley
Keyword(s):  
Excited State ◽  
Excited States ◽  
Quantum Algorithms ◽  
Reaction Rates ◽  
Mitigation Strategies ◽  
Quantum Computers ◽  
Error Mitigation ◽  
Near Term ◽  
Ground State Energies ◽  
High Depth

The calculation of excited state energies of electronic structure Hamiltonians has many important applications, such as the calculation of optical spectra and reaction rates. While low-depth quantum algorithms, such as the variational quantum eigenvalue solver (VQE), have been used to determine ground state energies, methods for calculating excited states currently involve the implementation of high-depth controlled-unitaries or a large number of additional samples. Here we show how overlap estimation can be used to deflate eigenstates once they are found, enabling the calculation of excited state energies and their degeneracies. We propose an implementation that requires the same number of qubits as VQE and at most twice the circuit depth. Our method is robust to control errors, is compatible with error-mitigation strategies and can be implemented on near-term quantum computers.

scholarly journals Entanglement-Free Parameter Estimation of Generalized Pauli Channels

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 490
Author(s):  
Junaid ur Rehman ◽  
Hyundong Shin
Keyword(s):  
Parameter Estimation ◽  
Measurement Errors ◽  
Quantum Algorithms ◽  
Constant Factor ◽  
Error Mitigation ◽  
Estimation Problems ◽  
Estimation Scheme ◽  
State Tomography ◽  
The Mean ◽  
Parameter Estimation Scheme

We propose a parameter estimation protocol for generalized Pauli channels acting on d-dimensional Hilbert space. The salient features of the proposed method include product probe states and measurements, the number of measurement configurations linear in d, minimal post-processing, and the scaling of the mean square error comparable to that of the entanglement-based parameter estimation scheme for generalized Pauli channels. We also show that while measuring generalized Pauli operators the errors caused by the Pauli noise can be modeled as measurement errors. This makes it possible to utilize the measurement error mitigation framework to mitigate the errors caused by the generalized Pauli channels. We use this result to mitigate noise on the probe states and recover the scaling of the noiseless probes, except with a noise strength-dependent constant factor. This method of modeling Pauli channel as measurement noise can also be of independent interest in other NISQ tasks, e.g., state tomography problems, variational quantum algorithms, and other channel estimation problems where Pauli measurements have the central role.

scholarly journals Fisher Information in Noisy Intermediate-Scale Quantum Applications

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 539
Author(s):  
Johannes Jakob Meyer
Keyword(s):  
Fisher Information ◽  
Quantum Algorithms ◽  
Quantum Fisher Information ◽  
Quantum Systems ◽  
Quantum Circuits ◽  
Quantum Computers ◽  
Quantum Devices ◽  
Intermediate Scale ◽  
Quantum Sensing ◽  
Near Term

The recent advent of noisy intermediate-scale quantum devices, especially near-term quantum computers, has sparked extensive research efforts concerned with their possible applications. At the forefront of the considered approaches are variational methods that use parametrized quantum circuits. The classical and quantum Fisher information are firmly rooted in the field of quantum sensing and have proven to be versatile tools to study such parametrized quantum systems. Their utility in the study of other applications of noisy intermediate-scale quantum devices, however, has only been discovered recently. Hoping to stimulate more such applications, this article aims to further popularize classical and quantum Fisher information as useful tools for near-term applications beyond quantum sensing. We start with a tutorial that builds an intuitive understanding of classical and quantum Fisher information and outlines how both quantities can be calculated on near-term devices. We also elucidate their relationship and how they are influenced by noise processes. Next, we give an overview of the core results of the quantum sensing literature and proceed to a comprehensive review of recent applications in variational quantum algorithms and quantum machine learning.

scholarly journals Error mitigation on a near-term quantum photonic device

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 452
Author(s):  
Daiqin Su ◽  
Robert Israel ◽  
Kunal Sharma ◽  
Haoyu Qi ◽  
Ish Dhand ◽  
...  
Keyword(s):  
Measurement Data ◽  
Photonic Devices ◽  
Error Correction Codes ◽  
Post Processing ◽  
Sampling Device ◽  
Error Mitigation ◽  
Hardware Resource ◽  
Near Term ◽  
Moderate Cost ◽  
Photon Loss

Photon loss is destructive to the performance of quantum photonic devices and therefore suppressing the effects of photon loss is paramount to photonic quantum technologies. We present two schemes to mitigate the effects of photon loss for a Gaussian Boson Sampling device, in particular, to improve the estimation of the sampling probabilities. Instead of using error correction codes which are expensive in terms of their hardware resource overhead, our schemes require only a small amount of hardware modifications or even no modification. Our loss-suppression techniques rely either on collecting additional measurement data or on classical post-processing once the measurement data is obtained. We show that with a moderate cost of classical post processing, the effects of photon loss can be significantly suppressed for a certain amount of loss. The proposed schemes are thus a key enabler for applications of near-term photonic quantum devices.

scholarly journals Variational Quantum Singular Value Decomposition

Quantum ◽  
2021 ◽  
Vol 5 ◽  
pp. 483
Author(s):  
Xin Wang ◽  
Zhixin Song ◽  
Youle Wang
Keyword(s):  
Singular Value Decomposition ◽  
Variational Principles ◽  
Quantum Algorithms ◽  
Singular Values ◽  
Singular Value ◽  
Quantum Devices ◽  
Singular Vectors ◽  
Fan Theorem ◽  
Near Term ◽  
Value Decomposition

Singular value decomposition is central to many problems in engineering and scientific fields. Several quantum algorithms have been proposed to determine the singular values and their associated singular vectors of a given matrix. Although these algorithms are promising, the required quantum subroutines and resources are too costly on near-term quantum devices. In this work, we propose a variational quantum algorithm for singular value decomposition (VQSVD). By exploiting the variational principles for singular values and the Ky Fan Theorem, we design a novel loss function such that two quantum neural networks (or parameterized quantum circuits) could be trained to learn the singular vectors and output the corresponding singular values. Furthermore, we conduct numerical simulations of VQSVD for random matrices as well as its applications in image compression of handwritten digits. Finally, we discuss the applications of our algorithm in recommendation systems and polar decomposition. Our work explores new avenues for quantum information processing beyond the conventional protocols that only works for Hermitian data, and reveals the capability of matrix decomposition on near-term quantum devices.

scholarly journals Hardware efficient quantum algorithms for vibrational structure calculations

2020 ◽  
Vol 11 (26) ◽  
pp. 6842-6855
Author(s):  
Pauline J. Ollitrault ◽  
Alberto Baiardi ◽  
Markus Reiher ◽  
Ivano Tavernelli
Keyword(s):  
Excited State ◽  
Quantum Algorithms ◽  
Vibrational Structure ◽  
Quantum Devices ◽  
Near Term ◽  
Structure Calculations ◽  
Vibrational Structure Calculations

We introduce a framework for the calculation of ground and excited state energies of bosonic systems suitable for near-term quantum devices and apply it to molecular vibrational anharmonic Hamiltonians.

scholarly journals Near-term quantum algorithms for linear systems of equations with regression loss functions

2021 ◽  
Vol 23 (11) ◽  
pp. 113021
Author(s):  
Hsin-Yuan Huang ◽  
Kishor Bharti ◽  
Patrick Rebentrost
Keyword(s):  
Linear Systems ◽  
Quantum Algorithms ◽  
Quantum Algorithm ◽  
Systems Of Equations ◽  
Quantum Devices ◽  
Near Term ◽  
Variational Algorithms ◽  
Core Idea ◽  
Classical Combination ◽  
Linear Systems Of Equations

Abstract Solving linear systems of equations is essential for many problems in science and technology, including problems in machine learning. Existing quantum algorithms have demonstrated the potential for large speedups, but the required quantum resources are not immediately available on near-term quantum devices. In this work, we study near-term quantum algorithms for linear systems of equations, with a focus on the two-norm and Tikhonov regression settings. We investigate the use of variational algorithms and analyze their optimization landscapes. There exist types of linear systems for which variational algorithms designed to avoid barren plateaus, such as properly-initialized imaginary time evolution and adiabatic-inspired optimization, suffer from a different plateau problem. To circumvent this issue, we design near-term algorithms based on a core idea: the classical combination of variational quantum states (CQS). We exhibit several provable guarantees for these algorithms, supported by the representation of the linear system on a so-called ansatz tree. The CQS approach and the ansatz tree also admit the systematic application of heuristic approaches, including a gradient-based search. We have conducted numerical experiments solving linear systems as large as 2300 × 2300 by considering cases where we can simulate the quantum algorithm efficiently on a classical computer. Our methods may provide benefits for solving linear systems within the reach of near-term quantum devices.

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